On Comparison of Series and Numerical Solutions for Flow of Eyring-Powell Fluid with Newtonian Heating And Internal Heat Generation/Absorption.

Tasawar Hayat,Ahmad Alsaedi,Shafqat Ali,Muhammad Asif Farooq,Zhong-Ke Gao

doi:10.1371/journal.pone.0129613

Abstract

In this paper, we have investigated the combined effects of Newtonian heating and internal heat generation/absorption in the two-dimensional flow of Eyring-Powell fluid over a stretching surface. The governing non-linear analysis of partial differential equations is reduced into the ordinary differential equations using similarity transformations. The resulting problems are computed for both series and numerical solutions. Series solution is constructed using homotopy analysis method (HAM) whereas numerical solution is presented by two different techniques namely shooting method and bvp4c. A comparison of homotopy solution with numerical solution is also tabulated. Both solutions are found in an excellent agreement. Dimensionless velocity and temperature profiles are plotted and discussed for various emerging physical parameters.

Highlights

Flow analysis of non-Newtonian fluid has received growing interest in the past few decades
Our interest further is concerned with the influence of parameters ε, δ, γ, λ and Pr on the velocity and temperature fields
Effects of heat source (λ > 0) and sink (λ < 0) on the temperature are analyzed in the Figs 5 and 6

Summary

Introduction

Flow analysis of non-Newtonian fluid has received growing interest in the past few decades. Layek et al [6] presented the boundary layer stagnation point flow towards a permeable stretching surface with heat and mass transfer. The objective of present communication is to explore the effect of Newtonian heating in the boundary layer flow of Eyring-Powell fluid [26] Consideration of this fluid has importance in the sense that it correctly reduces to viscous case at low and high shear rates. Further it is deduced from kinetic theory of liquids rather than the empirical relation. The first step for using bvp4c in MATLAB is to transform Eqs (7) and (8) into a system of first order ODEs

Shooting Method

Comparison and Discussion